# Probability question, The birthday problem

• Mar 20th 2010, 04:48 AM
RaVS
Probability question, The birthday problem
Two people enter a room and their birthdays (ignoring years) are recorded.
(a) Identify the nature of simple events in S.

(b) What is the probability that the two people have a specific pair of birth dates?

(c) Identify the simple events in event A:Both people have the same birthday.

(d)Find P(A)

(e) Find P(A^c)

Any help will be greatly appreciated,
cheers RaVS!
• Mar 21st 2010, 12:01 AM
CaptainBlack
Quote:

Originally Posted by RaVS
Two people enter a room and their birthdays (ignoring years) are recorded.
(a) Identify the nature of simple events in S.

(b) What is the probability that the two people have a specific pair of birth dates?

(a) The sample space is the set of all ordered pairs of birth days (that is if the two people are distinguishable) or of all sets of two birth days (if the people are not distinguishable the order of the dates is not relevant)

(b) Suppose the people are distinguishable, the first can gave any of $\displaystyle 365$ birthdays, and independently the second can have any of the $\displaystyle 365$ birthdays. All of these are equally likely so the number of possible pairs of birthdays is $\displaystyle 365 \times 365$, and as these are all equally likely the probability of any one is $\displaystyle 1/365^2$.

CB